Theorems · Theorem · commutative algebra
Valuation.vlt_one_iff
∀ {R : Type u_1} [inst : Ring R] [inst_1 : ValuativeRel R] {Γ₀ : Type u_2} [inst_2 : LinearOrderedCommMonoidWithZero Γ₀]
(v : Valuation R Γ₀) [v.Compatible] {x : R}, x <ᵥ 1 ↔ v x < 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- map_oneproof · cited by 861
- Valuationstatement and proof · cited by 823
- ValuativeRelstatement and proof · cited by 241
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.Compatiblestatement and proof · cited by 71
- ValuativeRel.vltstatement · cited by 49
- Valuation.vlt_iff_ltproof · cited by 2
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